Ros Hodgkiss and Jose Gross spoke to hundreds of wellwishers who had queued in driving rain to attend the humanist service in Greenford, west London, today.

They also heard from 14-year-old talented singer Alice herself, as two songs she had recorded were played, leaving many people in tears.

Her mother told the congregation: "I have been numbed by shock and grief, I have felt outrage and anger at the loss of her life and unbelievable sadness at the emptiness that has been left.

"I have wracked my brains for all the 'what ifs' of that day, anything that might have stopped this random, incomprehensible tragedy.

"It is even harder to talk about that pain than it is to talk about Alice. I cannot imagine life without Alice."

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Mrs Hodgkiss added that she would miss Alice most on all the special family occasions, like Christmas, Alice's birthday on Valentine's Day, Mothers' Day and her own birthday.

She said: "I think of all the ... hugs, shared jokes, evenings spent snuggled on the sofa, goodnight kisses, the confidence of after-school conversations, Alice playing the piano in her dressing gown (and) singing, shopping, baking, the way Alice still called me 'mummy'.

"The future seems bleak without Alice. It is only the incredible support of family friends and the wider community that has kept us going.

"We have been surrounded by people who have shown us that they cared, acts of individual kindness, a poster put up, a ribbon tied to a wall, thoughtful words, poem, shared condolence cards or Facebook message, flowers and teddies left as a tribute to Alice."

Alice was last seen alive walking along a tow path in west London on August 28, and it is believed that she was murdered by convicted killer Arnis Zalkalns, who was caught on CCTV following her on his bike.

Despite the biggest police search since the aftermath of the July 7 bombings, it was more than a month before her body was found weighted down in the bed of the River Brent, near where she lived in Hanwell.

Zalkalns, who had previously served seven years for murdering his wife Rudite in his native Latvia, was found hanged in nearby Boston Manor Park on October 4, four weeks after he was reported missing to the police.

Alice was buried 10 days ago in a private ceremony but her family held today's event to say thank you to all the people in the local community, who came together to help find her when she was missing and who rallied round after their worst fears were realised.

The service was played a recording of Alice singing and playing violin to Leonard Cohen's emotive song Hallelujah, with her father joining her on guitar.

A video was also shown on a big screen at Greenford Hall of her performing one of her own songs, called Don't Go Away, in a rich and powerful voice.

Jose Gross told the service it has been "very difficult to deal with this sudden, dramatic and tragic event", adding: "I cannot believe she is no longer here."

He spoke of walking her to primary school through woods and trees and how they both missed that time together.

He talked about how they had made music together, saying she was a "gifted musician and singer", who played piano, violin and ukulele and had started to learn the guitar.

He raised a laugh as he told how they had planned to play 'open mic' nights together, saying: "I think we would have been quite high in the 'aahhhh' factor, beautiful teenage daughter sings with old rock veteran dad."

He also paid tribute to the "extraordinary support" to him, his wife and Alice's sister Nina, which had grown from friends to strangers in the local community.

A Facebook page set up to help find Alice attracted 22,000 followers, yellow ribbons appeared tied to railings, buildings and other structures across the area and 6,000 runners in the Ealing Half Marathon also wore ribbons.

After her body was found Hanwell Clock Tower became a focus for tributes to her.

"The response of the community was astonishing," Mr Gross added. "I was amazed by how much people were touched by our ongoing tragedy and how much they cared.

"For five or so weeks the area became emblazoned in yellow ribbons, delivering a very powerful message of support to the public at large and anyone passing by. No one could pass through Hanwell and beyond without being aware that Alice was missing and that the community cared. When I felt very low the sight of the ribbons lifted my spirits."

Alice Gross

Nina did not speak at the event but a message was read out on her behalf by celebrant Caroline Black. In it she spoke of how Alice had made her laugh and their shared love of going for walks in the rain.

She added: "I wish I could have had one last chance to go on a walk with you in the pouring rain. The rain will not make me miserable like it does to most. It will make me smile as it reminds me of you."

Many of Alice's music teachers performed at the ceremony, with Serena Kay, her singing teacher, fighting back tears as she sang We're Walking In The Air, from the cartoon Christmas film The Snowman.

A sonnet written especially for the occasion by poet Brian Clark, was also read out by Julian Bell, the leader of Ealing Council.